Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments

2026-03-17

AI Summary

This work addresses the well-known limitation of convolutional neural networks (CNNs)—their sensitivity to input spatial translations due to downsampling operations that break translation invariance. To resolve this, the authors propose Gaussian-Hermite Sampling (GHS), a novel downsampling strategy that incorporates Gaussian-Hermite polynomials into the sampling process. Remarkably, GHS endows standard CNNs with strict translation invariance from the outset of training, without requiring any architectural modifications or changes to the training procedure. The method achieves 100% translation classification consistency on CIFAR-10, CIFAR-100, and MNIST-rot benchmarks while simultaneously improving overall classification accuracy, demonstrating that enforcing theoretical invariance at the sampling stage can yield both robustness and performance gains.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

The convolutional neural networks (CNNs) are not inherently shift invariant or equivariant. The downsampling operation, used in CNNs, is one of the key reasons which breaks the shift invariant property of a CNN. Conversely, downsampling operation is important to improve computational efficiency and increase the area of the receptive field for more contextual information. In this work, we propose Gaussian-Hermite Sampling (GHS), a novel downsampling strategy designed to achieve accurate shift invariance. GHS leverages Gaussian-Hermite polynomials to perform shift-consistent sampling, enabling CNN layers to maintain invariance to arbitrary spatial shifts prior to training. When integrated into standard CNN architectures, the proposed method embeds shift invariance directly at the layer level without requiring architectural modifications or additional training procedures. We evaluate the proposed approach on CIFAR-10, CIFAR-100, and MNIST-rot datasets. Experimental results demonstrate that GHS significantly improves shift consistency, achieving 100% classification consistency under spatial shifts, while also improving classification accuracy compared to baseline CNN models.

Problem

• shift invariance
• convolutional neural networks
• downsampling
• spatial shifts
• Gaussian-Hermite moments

Innovation

• Gaussian-Hermite Sampling
• shift invariance
• convolutional neural networks
• downsampling
• spatial consistency